Electrons trapped on the surface of liquid helium provide us with an extremely clean and controllable charge system [1]}. The surface-bound states of such electrons are formed due to their attraction to the induced image charges in the liquid and the hard-core repulsion from the helium atoms, which prevents the electrons to enter the liquid. The energy spectrum of such surface electrons (SE) consists of subbands of the quantized motion perpendicular to the surface and the free motion along the surface. The quantized Rydberg states of the perpendicular motion were proposed as an attractive system for qubit implementation, with a promise of sufficiently long coherence time of the qubit states [2]}. However, a recent study shows that the relaxation time of the excited Rydberg states is shorter than 1 \(\mu \) s due to the inelastic ripplon scattering of electrons from the surface-capillary waves (ripplons) [3]}. On the other hand, the spin states of surface electrons on liquid helium are expected to have longer coherence time (exceeding 100 s) than in any other solid-state materials, which makes them a viable resource for quantum computing [4]}. It was proposed that coupling of the spin states to the Rydberg states [5]} or the states of confined lateral motion of an electron [6]} can greatly facilitate the spin-state manipulation and detection, which would open a new pathway towards building a scalable quantum computer. In the above proposals, the spin-orbit coupling is introduced by creating a difference in the Zeeman splitting of the orbital states in a sufficiently strong gradient of the applied magnetic field. Most recently, the electrons trapped on solid neon were recognized as another promising platform for realizing the spin qubits [7]}.
